III. Turbulence in Two Dimensions

• A. Procedure
  • 1. Apparatus
  • 2. Shapes
• B. Results
• C. Analysis

A. Procedure

1. Apparatus

In order to study turbulence in two dimensions, a moving soap film was created by constructing the apparatus in Figure 6. There was a reservoir filled with a 2.5% soap solution (150 milliliters of soap in 6000 milliliters of water) which provided a continuous flow of solution to the testing component. The nine different wooden samples that were used were coated in a plastic covering which allowed for less surface friction. This was useful since only turbulence due to shape, not surface friction, was desired. The sample was dipped into the soap solution and placed on the sample support.

2. Shapes

To observe a range of different effects, nine shapes were cut from three-quarter inch wood (Figure 7, a-f; g-i on the following page). In order to be able to correlate the results of the two and three dimensional experiments, the sizes of the shapes in the three dimensional experiment were scaled down to use in the two dimensional experiment. The ratio of the size of the two dimensional shapes to the size of the three dimensional shapes was 31:160.

a) Sample 1

b) Sample 2

c) Sample 3

d) Sample 4

e) Sample 5

f) Sample 6
Figure 7: Shapes Put in the Soap Film (a-f)

B. Results

After setting up the device to study flow around a moving object, nine different shapes were used to observe fluid motion. The different types of flow: laminar and turbulent, as well as boundary layer behavior, were observed during testing.

Figure 8: (A) shockwaves, (B) wake area, (C) vortices
The laminar flow was almost transparent except for the streaks of color in the direction of the flow. This allowed for observation of the direction of flow when there were no disturbances in the fluid layers. As a result, disturbance was easily observed. Any circular or irregular motion in a nearly stagnant area of the film was detected as a slow swirling of color. The stronger, more erratic fluid motion distorted objects behind the film in the same manner as the distortion observed in heat waves above a flame. In the more extreme cases, the test was no longer two dimensional. Turbulence began to form a standing ripple in the film that appeared to be otherwise smooth, and, in some cases, the solution flowed over the front and back of the sample.
One of the simplest and most illustrative samples was the shorter of the two triangles (Figure 8). A shockwave (when the relative velocity of an object in a fluid is greater than the velocity of the waves of propagation moving through the fluid, shockwaves are created) was formed and a pocket of nearly stagnant film was created behind the sample. The fluid in this pocket moved in irregular patterns and generally moved toward the sample. There was a tendency at the vertices of the triangle for the solution immediately adjacent to the sample (the boundary layer) to form an eddy cycling from the flow to the base of the triangle. When the triangle was inverted so that the base was subjected to the flow, the observations were similar. The only difference was that a smooth layer of fluid propagated from the vertex.
The tear drop with both ends rounded also produced shockwaves and irregular motion in its wake (Figure 9). There were some undisturbed sheets of fluid behind the object, much like the motion generated by the triangle, only not as extreme. When this teardrop was inverted, the smooth flow at the center was even less noticeable. In both of these trials, fluid in the wake generally moved upward.

In these trials the behavior of the fluid passing the object followed several general trends. In the areas in the wake the fluid usually moved upward toward the sample in an otherwise random motion. In the boundary layer between the very regular flow of the shockwaves and the chaotic motion of the wake, the fluid changed its velocity vector to match that of the shockwave. It appeared that the fluid was being drawn outward and downward at an increasing speed as it moved towards a shockwave. Also, in the trials of shapes whose widest cross section was not at the lowest end, there was an area of regular flow trailing behind the lowest vertex of the sample. This indicates that some of the fluid was flowing along the surface of the object.

Figure 11: (A) shockwaves,
(B) wake area, (C) trailing flow,
(D) clockwise vortex, (E) turbulent area
When the thin rectangle was tested perpendicular to the direction of flow, its behavior was the same as that of the shorter triangle, except that the vortices produced by the former were larger and moved more slowly. The behavior changed dramatically when its angle of incidence was changed, as shown in Figure 11. One change was that, in the area where the shockwave hit the surface of the sample, the motion was extremely chaotic but still had a general rolling cyclic motion. The fluid showed a tendency to follow the surface of the rectangle; yet, in these trials the fluid seemed to flow along the lower surface, which, in this angled orientation, was one of the longer sides. It did not, however, flow along the lower narrow side of the rectangle. This fluid seemed to be drawn to the shockwave propagating from the upper surface. In this area the flow was unstable and fluctuated quickly but maintained a vortex drawing from the lower current and feeding into the shockwave, creating in this orientation a clockwise rotation. Where the flow from the lower surface and the shockwave met, some very erratic motion was created.
When other shapes were put in the soap film at an angle, some interesting observations were made. Although this information did not contribute to the results because the tilted shapes were more difficult to generalize, the fluid flow that occurred was worth noting (Figures 12 and 13 on the following page).

Figure 12: (A) shockwaves, (B) trailing flow, (C) wake area, (D), slow stationary eddy, (E) rapid cyclic motion

Figure 13: (A) shockwaves, (B) slowly curving flow, (C) wake area

C. Analysis

Through observing the motion of the film surrounding the shapes, one can conclude that the shockwaves, and therefore the area of the wake, are affected most by the shape of the object above the maximum cross section since the shockwaves observed roughly followed the shape's tangents at this point. Similarly, the behavior of the fluid in the wake is most affected by the shape of the object below the maximum cross-section.
This became evident in the teardrop tests. The front of these objects were exactly the same shape as the half circle. They had a diameter of 4.5 cm and they all had similar shockwaves (Table 1). Each shockwave began to propagate at or near the maximum width of cross section. Also, the diamond and the two triangles, which were similar in shape above the maximum cross section, all produced shockwaves that followed the shape's tangent line at the maximum cross sectional width.
The behavior of the wake was most affected by a different factor. Note in the forward test of the teardrops and the half circle, the behavior of the wakes was different. As the shape becomes more tapered below the maximum cross sectional width, the flow of the wake tends to follow the surface of the sample more closely. This draws flow away from the shockwaves, reducing the amount of drag. For example, the fluid did not flow along the surface of the double rounded teardrop very well, but the teardrop with a downward point was very conducive to this type of flow.
Further, it can be observed that if the shapes are lengthened, the amount of disturbance created by the passage of the object is reduced. If the top portion of the shape is elongated, the shockwaves propagate at smaller angles, thus reducing the area of the wake. This, as a result, reduces the drag because there is less disturbance in the flow of the fluid. In the trials with the triangles vertex-forward, the longer triangle had a narrower wake. If the length of the shape below the maximum cross section is increased, more of the fluid follows the surface of the sample, drawing even more of the flow from the shockwaves. Conversely, if the lower portion of this shape is shortened, the fluid will follow the surface less and, therefore, strengthen the shockwave. This behavior was observed in the tests of the triangle base forward samples. The flow around the longer triangle followed its surface more than the flow around the shorter triangle.
The smallest shockwave was created by shapes with round frontal surfaces and there was the least amount of disturbance in the wake of the shapes whose lower ends were longer. It would seem likely, then, that the most aerodynamically successful shape would be a very elongated teardrop (half of an oval on the top and a point on the bottom). In contrast, the shape with the most drag, and therefore the least aerodynamic value, might have a concave arch facing the fluid flow and a straight line at the back. This is supported by the cases of the half circle with the arched side forward and the triangle with the base forward. The shockwave was bigger in the latter case, as was the amount of disturbance in the fluid flow. This indicates that the more concave the front of the shape becomes, the larger its drag and the worse it performs aerodynamically.
One important aspect, as well as advantage, of this experiment is its reproducibility. Samples could be tested multiple times and the same observations were made.